An axiomatization of the Myerson value
Contributions to game theory and management, Tome 7 (2014), pp. 341-348.

Voir la notice de l'article provenant de la source Math-Net.Ru

TU-games with communication structure are cooperative games with transferable utility where the cooperation between players is limited by a communication structure represented by a graph on the set of players. On this class of games, the Myerson value is one of the most well-known solutions and it is the Shapley value of the so-called restricted game. In this study we give another form of fairness axiom on the class of TU-games with communication structure so that the Myerson value is uniquely characterized by this fainess axiom with (component) efficiency, a kind of null player property and additivity. The combination is similar to the original characterization of the Shapley value.
Keywords: Cooperative TU-games, communication structure, Myerson value, Shapley value.
@article{CGTM_2014_7_a30,
     author = {\"Ozer Sel\c{c}uk and Takamasa Suzuki},
     title = {An axiomatization of the {Myerson} value},
     journal = {Contributions to game theory and management},
     pages = {341--348},
     publisher = {mathdoc},
     volume = {7},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2014_7_a30/}
}
TY  - JOUR
AU  - Özer Selçuk
AU  - Takamasa Suzuki
TI  - An axiomatization of the Myerson value
JO  - Contributions to game theory and management
PY  - 2014
SP  - 341
EP  - 348
VL  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CGTM_2014_7_a30/
LA  - en
ID  - CGTM_2014_7_a30
ER  - 
%0 Journal Article
%A Özer Selçuk
%A Takamasa Suzuki
%T An axiomatization of the Myerson value
%J Contributions to game theory and management
%D 2014
%P 341-348
%V 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CGTM_2014_7_a30/
%G en
%F CGTM_2014_7_a30
Özer Selçuk; Takamasa Suzuki. An axiomatization of the Myerson value. Contributions to game theory and management, Tome 7 (2014), pp. 341-348. http://geodesic.mathdoc.fr/item/CGTM_2014_7_a30/

[1] Borm P., Owen G., Tijs S., “On the position value for communication situations”, SIAM Journal of Discrete Mathematics, 5 (1992), 305–320 | DOI | MR | Zbl

[2] Brink R. van den, “An axiomatization of the Shapley value using a fairness property”, International Journal of Game Theory, 30 (2002), 309–319 | DOI | MR

[3] Brink R. van den, Comparable axiomatizations of the Myerson value, the restricted Banzhaf value, hierarchical outcomes and the average tree solution for cycle-free graph restricted games, Tinbergen Institute Discussion Paper 2009-108/1, Tinbergen Institute, Amsterdam, 2009

[4] Myerson R. B., “Graphs and cooperation in games”, Mathematics of Operations Research, 2 (1977), 225–229 | DOI | MR | Zbl

[5] Shapley L., “A value for $n$-person games”, Contributions to the Theory of Games, v. II, eds. Kuhn H. W., Tucker A. W., Princeton University Press, Princeton, 1953, 307–317 | MR

[6] Young H. P., “Monotonic solutions of cooperative games”, International Journal of Game Theory, 14 (1985), 65–72 | DOI | MR | Zbl